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Apparatus to Study Action Potentials Stimulus and Response Trace #1 (near stimulator) -60 Trace #2 (further from stim.) -60 Em (mV) -70 -70 stimulus knp stimulus Membrane Model outside DC Generator Cm Rm Membrane (between dotted lines) (+) (-) knp B inside The dc generator is very low capacity. What does this means (structurally)? Membrane Components + + + 3Na+ + + + + Na+/K+ ATPase + + Ion Channel or Gate excess + ions + + + + + knp - - - - excess neg. ions - - - - ADP + Pi - 2 K+ ATP - - - Action Potentials Trace #1 (near stimulator) +35 0 Em (mV) -70 Voltage knp Trace #2 (further from stim.) +35 0 -70 stimulus Active Responses Trace #1 (near stimulator) -60 Trace #2 (further from stim.) -60 Em (mV) -70 Voltage knp -70 1.25X stimulus APs at Above Threshold Stimuli Trace #1 (near stimulator) +35 0 Em (mV) -70 Voltage knp Trace #2 (further from stim.) +35 0 -70 stimulus Graded vs. Action Potentials The Events of an Action Potential +50 0 Em -50 threshold rmp -100 knp negative after potential (hyperpolarized) time Membrane Model #2 RK+ RCl- RNa+ Cm B K+ B Cl- B Na+ This model is valid ONLY for a very thin section of the length of an axon (or muscle fiber). This sort of model was hypothesized by the late 1940s The Voltage Clamp, part 1 In order for Em to change, the total charge (Q) across the membrane capacitance (Cm) must change. For Q to change, a current must flow. (Obviously!) However, any current associated with the membrane has two components: • one associated with charging or discharging the Cm (called iC) • another, iR, associated with current flow through the various parallel membrane resistances, lumped together as RM. • Thus: i = i + i M C R The Voltage Clamp, part 2 We can only measure TOTAL membrane current, im directly. But, we are most interested in the "resistive" current components because these are associated with ionic movements through channels and gates. -- Is there a way to separate ir from the capacitive current, iC? The Voltage Clamp, part 3 Recall that: QC EC * CM VC * CM If we take the time derivative of the last equation (to get current flowing in or out of the capacitance, ic): dQc dVc CM dt dt dVc iC CM dt The Voltage Clamp, part 4 If we substitute the expression for iC (last slide) into the total membrane current equation, we get: dV im i R CM dT Reminder: total membrane current, im, is: im iR iC If there is some way to keep the transmembrane potential (Em) constant (dV/dt=0) then: im iR Thus, if EM is constant, then any current we measures is moving through the membrane resistance(s) –i.e., these currents are due to specific ions moving through specific types of channels. How can we keep Em constant during a time (the AP) when Em normally changes rapidly? Answer: we use a device called the voltage clamp to deliver a current to the inside of the cell -- initially to change Em to some new “clamped” voltage and then in such a way as to prevent Em from changing – i.e., in a way to hold Em constant. • The clamp senses minute changes in (dEm) due to ions moving through membrane channels (rm) and into or out of the membrane capacitor, Cm. • The clamp applies charge to the electrodes (a current) to stop this movement and keep Em essentially constant. Thus, capacitive current is zero as is the resistive current. Whatever current was applied by the clamp was equal and opposite to whatever im “tried” to flow. A Drawing of the Voltage Clamp More on the Voltage Clamp Clamp Electrode Clamp Electrode outside outside + + + + + inside inside K+ K+ K+ K+ K+ K+ K+ K+ K+ K+ knp Assume that for both situations conditions are such that K+ movement out of the cell is favored. In the first case, if the electrode is off, the K+ diffuses out down the electrochemical gradient creating a certain current, iK+. In the second case, a current is applied by the electrode that is equal and opposite to iK+ and there is no net outward movement of K+. Review of Membrane Model RK+ RCl- RNa+ Cm B K+ B Cl- B Na+ Let’s review what we think we know about current flows in a resting cell. Idealized Voltage Clamp, subthreshold Curre nt Out 2 mV 1 mv 0 tim e In knp The Events of an Action Potential +50 0 Em -50 threshold rmp -100 knp negative after potential (hyperpolarized) time Voltage Clamp Data for a Stimulus that Would Elicit an AP in a Non-Clamped Cell out Super-threshold stimulus delivered clamp at +10 mV clamp at 0 mV 0 knp in Both of these clamp Em values are well above threshold and would normally elicit an AP. Same Stimulus as Previous But No Na+ Current Current (Direction and Magnitude) Inward and Outward Currents at Two Clamp Potentials out IK+ curves clamp = +10mV clamp = 0 mV 0 clamp = +10 mV INa+ Curves knp clamp = 0 mV in Clamp At Local Potential Values Current Out - 64 mV - 65mV 0 In knp time Outward Current Only At Local Potential Clamp Values Curre nt Out - 64 m V - 65m V 0 In knp tim e Clamp at High Depolarizations + 100 Curre nt +0 Out 0 In knp + 55 + 40 tim e Outward Currents at High Clamp Depolarizations + 100 Curre nt +0 Out 0 In knp + 55 + 40 tim e Using Clamp Data to Find Membrane Conductances Ohm’s Law: iion = Eion * R-1ion The emf for a particular ion (Eion) is the difference between Em and the ion's Nernst potential. Thus: iion = Gion * (Em - Eion) Calculation of the Conductance Changes During an AP We must calculate the conductances (G) for each ion with respect to time. To do this, you simply use the conductance equation with the clamp voltage as Em, the ion’s Donnan equilibrium voltage and the current (calculated from voltage clamp data) at any moment of time Thus: Gion at time t = (iion at time t )/ (Em - Eion) Conductances During An AP Finding Em with the Goldman-Hodgkin-Katz Equation (a.k.a. Goldman or Goldman Field eq.) EM 58 *log Gcation1 *[cation1 ]in Gcation2 *[cation2 ]in Ganion1 *[anion1 ]out Gcation1 *[cation1 ]out Gcation2 *[cation2 ]out Ganion1 *[anion1 ]in Our Latest Membrane Model RK+ RCl- RNa+ Cm B K+ B Cl- Could this be further modified? B Na+ Populations of Channels and Voltage-Gated Channels How do we modify our model to take into account several types of K+ channels?